CN108536943B - Fault monitoring method based on multi-production-unit variable cross-correlation decoupling strategy - Google Patents

Abstract

The invention discloses a fault monitoring method based on a multi-production-unit variable cross correlation decoupling strategy, and aims to consider the cross relationship among different production units in an industrial object into a distributed modeling and monitoring process from the data perspective so as to implement more reliable and effective distributed fault monitoring. Specifically, firstly, dividing all measurement variables into a plurality of variable sub-blocks according to the attribution of the measurement variables of each production unit; secondly, mining cross-correlation information between each variable subblock and other variable subblocks by using a regression model; and finally, modeling and fault monitoring are implemented by using the error after cross correlation decoupling. Compared with the traditional method, the method provided by the invention takes the cross relationship among the variable sub-blocks of different production units into consideration by utilizing the regression model, and monitors the error which can reflect whether the cross correlation among the different production units changes, so that the fault monitoring performance is better.

Description

Fault monitoring method based on multi-production-unit variable cross-correlation decoupling strategy

Technical Field

The invention relates to a data-driven fault monitoring method, in particular to a fault monitoring method based on a multi-production-unit variable cross correlation decoupling strategy.

Background

The continuous normal production state is important for reducing the production cost of enterprises and ensuring the production safety, and the usually adopted technical means can not be used for monitoring the process running state in real time, so that the abnormal state of the system can be screened out in time. In recent years, with the promotion of large-scale industrial and large-data construction, a large amount of real-time data can be collected in the production process, and an accurate mechanism model cannot be established, so that the method lays foundation for the rising and wide application of a data-driven fault monitoring method. Multivariate statistical process monitoring has received the most research and attention in this field of research. Among these, the Principal Component Analysis (PCA) algorithm is the most popular implementation technique. By mining the potential features of the training data, the PCA-based fault monitoring method converts the fault monitoring task into a single-classification pattern recognition problem. In this respect, the core of the PCA-based fault monitoring methodology lies in how to effectively describe the correlation between the sampled data.

Furthermore, given the large scale of modern industrial processes, PCA-based fault monitoring methods have evolved from the first single fault monitoring model to distributed fault monitoring strategies. Generally speaking, a distributed fault monitoring method can simplify the difficulty of process object analysis during modeling, and the idea of multiple models is generally superior to that of a single model in generalization performance. Due to the large-scale trend of modern industrial processes, the entire production unit is usually composed of a number of sub-production units. Therefore, it is the core essence of the distributed fault monitoring method that all the measurement variables can be divided into a plurality of sub-variable blocks according to the attribution of the production units, and then each sub-variable block is monitored.

However, in modern industrial processes, there are also cross-relationships between the production subunits, such as the backflow of products into other production units, and the use of feedback signals between different production units for control, etc. The fact of dividing the production units into variable sub-blocks directly does not take into account the cross-relationships between different production units. Therefore, the conventional distributed fault monitoring method still needs to be further improved. If the distributed fault monitoring is implemented according to the production units, the cross-correlation relationship among different production units can be taken into consideration, and the performance of the corresponding fault monitoring method can be improved. However, if such a cross-correlation is directly analyzed based on the knowledge of the mechanism of the production process, it is necessary to deeply and carefully analyze the structural configuration of the process object. This is not desirable in practice and also violates the idea of data-driven failure monitoring methods from a data perspective.

Disclosure of Invention

The invention aims to solve the main technical problems that: from the data perspective, the cross relationship between different production units in the industrial object is considered in the distributed modeling and monitoring process, so that more reliable and effective distributed fault monitoring is implemented. Specifically, the method comprises the steps of dividing all measurement variables into a plurality of variable sub-blocks according to the attribution of the measurement variables of each production unit; secondly, mining cross-correlation information between each variable subblock and other variable subblocks by using a regression model; and finally, modeling and fault monitoring are implemented by using the error after cross correlation decoupling.

The technical scheme adopted by the invention for solving the technical problems is as follows: a fault monitoring method based on a multi-production-unit variable cross correlation decoupling strategy comprises the following steps:

(1) collecting sample data of all production units in the production process object under normal operation state to form a training data set X belonging to R^n×mAnd carrying out standardization processing on the data matrix to obtain a new data matrix with the mean value of 0 and the standard deviation of 1

Wherein n is the total number of training samples, m is the number of all measured variables of the process object, R is a real number set, R^n×mRepresenting a matrix of real numbers in dimension n x m.

(2) According to the production unit attribution of each measurement variable, dividing m measurement variables into C different variable sub-blocks, wherein C represents the number of production units in the process object.

(3) Matrix matching according to C different variable sub-blocks

Divided correspondingly into C different sub-matrices X₁，X₂，…，X_CWherein

c＝1，2，…，C，m_cThe number of variables in the c variable sub-block meets the condition sigma m_c＝m。

(4) The c sub-matrix X_cAs the output of the regression model, Y ═ X simultaneously₁，…，X_c-1，X_c+1，…X_C]As an input of the regression model, a Partial Least Squares (PLS) algorithm is used to establish a regression model between input and output, and the specific implementation process is as follows:

after k is equal to 1 and Z is equal to Y, the vector u is initialized_kIs a matrix X_cThe first column of (1);

② according to the formula w_k＝Zu_k/||Zu_k||、s_k＝Zw_k、q_k＝X_c ^Ts_k/(s_k ^Ts_k) Respectively calculating to obtain coefficient vectors w_kScore vector s_kAnd a sum coefficient vector q_kWherein | | | Zu_kI represents the calculated vector Z_iu_kThe upper label T represents the transpose of a matrix or vector;

③ according to formula u_new＝X_cq_k/q_k ²Calculating the vector u_new；

Fourthly, judging whether the condition is satisfied | | | u_k-u_new||＜10^-6Is there a If not, put u_k＝u_newThen returning to the step II; if yes, executing a fifth step;

fifthly, according to the formula p_k＝Z^Ts_k/(s_k ^Ts_k) Calculating to obtain the k-th projection vector p_k∈R^(m-1)×1And retaining the vector p_kVector w_kAnd a sum coefficient vector q_k；

Sixth, judge matrix Y_k＝s_kp_k ^TIs the largest element in (a) greater than 0.01? If so, according to the formula Z-S_kp_k ^TUpdating the matrix Z_iPerforming step (c); if not, obtaining a projection matrix P ═ P₁，p₂，…，p_k]And the coefficient matrix W ═ W₁，w₂，…，w_k]And the vector Q ═ Q₁，q₂，…，q_k]And executing the step (b);

seventhly, judging that k is less than m-m_cIs there a If yes, after k is set to k +1, returning to the step II; if not, the final projection matrix P is obtained as [ P ]₁，p₂，…，p_k]And the coefficient matrix W ═ W₁，w₂，…，w_k]And the vector Q ═ Q₁，q₂，…，q_k]；

According to formula b_r＝W_r(P_r ^TW_r)^-1Q_r ^TCalculating a regression coefficient vector b under the condition of reserving r projection vectors_rWherein r is 1, 2, …, k, P_r、W_rAnd Q_rThe matrix P, W and the matrix formed by the vectors of the first 1 to r columns in Q respectively;

ninthly according to the formula

Computing output X_cPredicted value of (2)

Then, model prediction errors corresponding to different numbers of projection vectors are calculated and reserved

Wherein diag 2]Representing the operation of independently forming elements of a diagonal line of the matrix into a vector, and sum { } represents the summation of each element in the vector;

in the r in accordance with MSE₁，MSE₂，…，MSE_kFinding out the position of a convergence point of which the prediction error does not change remarkably any more according to the change condition of the numerical value, and taking a specific numerical value corresponding to a subscript number of the convergence point as the number K of projection variables needing to be reserved by the partial least square model, wherein K is less than or equal to K;

determining final input Y and output X according to K_cThe PLS model in between, namely:

X_c＝YW_K(P_K ^TW_K)^-1Q_K ^T+E_c＝YΘ_c+E_c (1)

in the above formula, theta_c＝W_k(P_K ^TW_k)^-1Q_K ^T，

Is the regression model error;

(5) repeating the step (4) until C PLS models are obtained, and correcting the model error E₁，E₂，…，E_CAre combined into an error matrix E ═ E₁，E₂，…，E_C]∈R^n×m。

(6) Taking the estimated error matrix E as a new training data matrix, and carrying out standardization processing on each column to obtain a new data matrix with the mean value of 0 and the standard deviation of 1

(7) Using a PCA algorithm of

Establishing a corresponding PCA fault monitoring model, and reserving a model parameter set theta ═ B, Lambda, D_lim，SPE_limB is projection variable matrix, Λ is diagonal matrix composed of eigenvalues, D_limAnd SPE_limRespectively representing the upper control limits of the monitoring statistic D and the SPE, and the specific implementation process is as follows:

calculating

Covariance matrix of

Solving all the characteristic values gamma of S₁≥γ₂≥…≥γ_mCorresponding feature vector beta₁，β₂…，β_m；

Setting the number d of the reserved main components as the minimum value meeting the following conditions, and forming a diagonal matrix Lambda epsilon R by the corresponding d maximum eigenvalues^d×dAnd forming a projection transformation matrix B ═ beta by the corresponding d eigenvectors₁，β₂…，β_d]

Fourthly, D is calculated according to the formula shown in the specification_limAnd SPE_lim：

In the above two formulae, the confidence level α is 99%, F_α(d, n-d) represents a F distribution with degrees of freedom d and n-d,

represents the weight g ═ a/2b, and the degree of freedom h ═ 2a²χ of/b²Distribution, a and b are respectively

The estimated mean and the estimated variance of the corresponding statistic SPE.

(8) Collecting data sample x ∈ R at new sampling moment^1×mSubjecting it to the same normalization process as in step (1) to obtain a new data vector

(9) Correspondingly vector the samples according to the C different variable sub-blocks in the step (2)

Into C different sub-vectors x₁，x₂，…，x_C。

(10) Calling the c PLS model established in the step (4), and calculating the error e after cross correlation decoupling of the variables of the multiple production units according to the formula shown below_c

e_c＝x_c-yΘ_c (5)

In the above formula, y ═ x₁，…，x_c-1，x_c+1，，x_C]。

(11) Repeating the step (10) until C errors e are obtained₁，e₂，…，e_CAnd combines these errors into an error vector e ═ e₁，e₂，…，e_C]。

(12) The error e is normalized in the same manner as in the step (6) to obtain a new vector

(13) And calculating the monitoring statistical indexes D and SPE according to the following formula:

in the above formula, I is an m × m dimensional identity matrix.

(14) Judging whether the conditions are met: d is less than or equal to D_limAnd SPE is not less than SPE_limIs there a If yes, the system is in a normal operation state at the current monitoring moment, and the step (8) is returned to continue to implement online fault monitoring; if not, the current sampling data comes from the fault working condition.

Compared with the traditional method, the method has the advantages that:

the method of the invention takes the cross relationship between the variable sub-blocks of different production units into consideration by using the regression model, rather than directly establishing a distributed multiple fault monitoring model. Because the error of the regression model contains information irrelevant to the model input, the error information utilized by the method is the component information after variable cross-correlation decoupling of the multiple production units, and whether the cross-correlation relationship between different production units changes can be reflected. In addition, the method carries out modeling and monitoring on the error based on the PCA algorithm, and can also excavate the correlation characteristics among error information. Therefore, the method of the present invention is a more preferable data-driven fault monitoring method, which has better fault monitoring performance.

Drawings

FIG. 1 is a flow chart of the method of the present invention.

Fig. 2 is a flow chart of the TE process structure.

FIG. 3 is a schematic cross-correlation decoupling.

FIG. 4 is a comparison graph of fault monitoring details of inlet temperature fault changes of TE process material C.

Detailed Description

The method of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

As shown in fig. 1, a fault monitoring method based on a multi-production unit variable cross-correlation decoupling strategy. The following description will be made with reference to an example of a specific industrial process, and the implementation of the method of the present invention and its advantages over the conventional distributed PCA method.

The application object is from the U.S. Tennessee-Ismann (TE) chemical process experiment, and the prototype is a practical process flow of an Ismann chemical production workshop. As shown in fig. 2, the production flow of the TE process is relatively complex, and includes 5 main production units: a reactor, a condenser, a separation column, a stripper, and a compressor. The TE process has been widely used for fault monitoring research as a standard experimental platform, and the whole TE process includes 22 measurement variables, 12 operation variables, and 19 component measurement variables. 33 process variables shown in table 1 are selected to implement offline modeling and online fault monitoring, and then the specific implementation steps of the invention are elaborated in detail by combining the TE process.

Table 1: the TE process monitors variables.

Serial number	Description of variables	Serial number	Description of variables	Serial number	Description of variables
						1	Flow rate of material A	12	Liquid level of separator	23	D feed valve position
2	Flow rate of material D	13	Pressure of separator	24	E feed valve position
						3	Flow rate of material E	14	Bottom flow of separator	25	A feed valve position
4	Total feed flow	15	Stripper grade	26	A and C feed valve position
						5	Flow rate of circulation	16	Stripper pressure	27	Compressor cycling valve position
6	Reactor feed	17	Bottom flow of stripping tower	28	Evacuation valve position
						7	Reactor pressure	18	Stripper temperature	29	Separator liquid phase valve position
8	Reactor grade	19	Stripping tower overhead steam	30	Stripper liquid phase valve position
						9	Reactor temperature	20	Compressor power	31	Stripper steam valve position
10	Rate of emptying	21	Reactor cooling water outlet temperature	32	Reactor condensate flow
						11	Separator temperature	22	Separator cooling water outlet temperature	33	Flow rate of cooling water of condenser

Firstly, a fault monitoring model is established offline by utilizing sampling data under the normal working condition of a TE process, and the method comprises the following steps:

(1): collecting data samples in normal operation state of production process to form training data set X belonging to R^960×33And standardizing each variable to obtain a new data matrix with a mean value of 0 and a standard deviation of 1

Table 2: and dividing the variable sub-block of the multiple production units into results.

Name of production unit:	variable number in variable sub-block:
		reactor with a reactor shell	1，2，3，6，7，8，9，21，23，24，25，32
Condenser	33
		Separation tower	4，15，16，17，18，19，26，30，31
Stripping tower	10，11，12，13，14，22，28，28
		Compressor	5，20，27

(2): according to the production unit attribution of each measurement variable, 33 measurement variables are divided into 5 different variable sub-blocks, and the division results of the corresponding variable sub-blocks are shown in table 2.

(3): matrix matching according to 5 different variable sub-blocks

Divided correspondingly into 5 different sub-matrices X₁，X₂，…，X₅。

(4): the c sub-matrix X_cAs the output of the regression model, Y ═ X simultaneously₁，…，X_c-1，X_c+1，…X₅]As input to the regression model, a PLS algorithm was used to build a regression model between input-output: x_c＝YΘ_c+E_c。

(5): repeating the step (4) until 5 PLS models are obtained, and correcting the model error E₁，E₂，…，E₅Are combined into an error matrix E ═ E₁，E₂，…，E₅]。

To verify the cross-correlation decoupling properties, E₅And input Y ═ X₁，X₂，X₃，X₄]A schematic diagram of cross-correlation decoupling between them is shown in fig. 3. From fig. 3 it can be seen that the compressor production unit corresponds to an error E₅The time sequence correlation between the measured variables of other production units is almost all 0, namely, cross correlation decoupling is embodied.

(6): and taking the estimation error matrix E as a new training data matrix, and carrying out standardization processing on the estimation error matrix E.

(7): is composed of

Establishing a corresponding PCA fault monitoring model, and reserving a model parameter set theta ═ B, Lambda, D_lim，SPE_lim}。

And (3) utilizing the sampling data of the inlet temperature fault variable working condition of the TE process material C as test data to implement online fault monitoring. It is worth noting that the first 160 data of the test data set are normal conditions and fault conditions are introduced from 161 data sampling instants.

(8): collecting data sample x ∈ R at new sampling moment^1×33Subjecting it to the same normalization process as in step (1) to obtain a new data vector

After that, i is initialized to 1.

(9): according to 5 different variables in step (2)Sub-blocks correspondingly vector samples

Divided correspondingly into 5 different subvectors x₁，x₂，…，x₅；

(10): calling the c PLS model established in the step (4), and calculating the error e after cross correlation decoupling of the variables of the multiple production units according to the formula shown below_c。

(11): repeating the step (10) until 5 errors e are obtained₁，e₂，…，e₅And combines these errors into an error vector e ═ e₁，e₂，…，e₅]。

(12): the error e is normalized in the same manner as in the step (6) to obtain a new vector

(13): and calculating monitoring statistical indexes D and SPE.

(14): judging whether the conditions are met: d is less than or equal to D_limAnd SPE is not less than SPE_limIs there a If yes, the system is in a normal operation state at the current monitoring moment, and the step (8) is returned to continue to implement online fault monitoring; if not, the current sampling data comes from the fault working condition.

As shown in fig. 4, a comparison graph of the monitoring details of the method of the present invention and the conventional distributed PCA method on the test fault shows that the fault failure rate of the method of the present invention is obviously lower than that of the conventional distributed PCA method. Therefore, the monitoring effect of the method is superior to that of the traditional distributed PCA fault monitoring method.

The above embodiments are merely illustrative of specific implementations of the present invention and are not intended to limit the present invention. Any modification of the present invention within the spirit of the present invention and the scope of the claims will fall within the scope of the present invention.

Claims (3)

1. A fault monitoring method based on a multi-production-unit variable cross correlation decoupling strategy is characterized by comprising the following steps:

the implementation of the offline modeling is as follows:

step (1): collecting sample data of all production units in the production process object under normal operation state to form a training data set X belonging to R^n×mAnd carrying out standardization processing on the data matrix to obtain a new data matrix with the mean value of 0 and the standard deviation of 1

Wherein n is the total number of training samples, m is the number of all measured variables of the process object, R is a real number set, R^n×mA real number matrix representing dimensions n × m;

step (2): dividing m measurement variables into C different variable sub-blocks according to the attribution of the production units of the measurement variables, wherein C represents the number of the production units in the process object;

and (3): matrix matching according to C different variable sub-blocks

Divided correspondingly into C different sub-matrices X₁，X₂，…，X_CWherein

m_cThe number of variables in the c variable sub-block meets the condition sigma m_c＝m；

And (4): the c sub-matrix X_cAs the output of the regression model, Y ═ X simultaneously₁，…，X_c-1，X_c+1，…X_C]As an input to the regression model, a partial least squares algorithm is used to build a regression model between input and output as shown below:

X_c＝YΘ_c+E_c (1)

in the above formula, theta_cIn the form of a regression matrix,

is the regression model error;

and (5): repeating the step (4) until C PLS models are obtained, and correcting the model error E₁，E₂，…，E_CAre combined into an error matrix E ═ E₁，E₂，…，E_C]∈R^n×m；

And (6): taking the error matrix E as a new training data matrix, and carrying out standardization processing on each column to obtain a new data matrix with a mean value of 0 and a standard deviation of 1

And (7): using a principal component analysis algorithm of

Establishing a corresponding PCA fault monitoring model, and reserving a model parameter set theta ═ B, Lambda, D_lim，SPE_limB is projection variable matrix, Λ is diagonal matrix composed of eigenvalues, D_limAnd SPE_limRespectively representing the upper control limits of the monitoring statistic D and the SPE;

the implementation process of online fault monitoring is as follows:

and (8): collecting data sample x ∈ R at new sampling moment^1×mSubjecting it to the same normalization process as in step (1) to obtain a new data vector

And (9): correspondingly adding new data vectors according to the C different variable sub-blocks in the step (2)

Into C different sub-vectors x₁，x₂，…，x_C；

Step (10): calling the c PLS model established in the step (4), and calculating the cross correlation decoupling of variables of multiple production units according to the formula shown in the specificationError e of_c

e_c＝x_c-yΘ_c (5)

In the above formula, y ═ x₁，…，x_c-1，x_c+1，x_C]；

Step (11): repeating the step (10) until C errors e are obtained₁，e₂，…，e_CAnd combines these errors into an error vector e ═ e₁，e₂，…，e_C]；

Step (12): the error vector e is normalized in the same manner as in the step (6) to obtain a new vector

Step (13): and calculating the monitoring statistical indexes D and SPE according to the following formula:

in the above formula, I is an m × m dimensional unit matrix;

step (14): judging whether the conditions are met: d is less than or equal to D_limAnd SPE is not less than SPE_lim(ii) a If yes, the system is in a normal operation state at the current monitoring moment, and the step (8) is returned to continue to implement online fault monitoring; if not, the current sampling data comes from the fault working condition.

2. The fault monitoring method based on the multi-production-unit variable cross-correlation decoupling strategy as claimed in claim 1, wherein the step (4) is implemented by using a partial least squares algorithm to establish the input Y and the output X_cThe implementation steps of the regression model are as follows:

after k is equal to 1 and Z is equal to Y, the vector u is initialized_kIs a matrix X_cThe first column of (1);

② according to the formula w_k＝Zu_k/||Zu_k||、s_k＝Zw_k、q_k＝X_c ^Ts_k/(s_k ^Ts_k) Respectively calculating to obtain coefficient vectors w_kScore vector s_kAnd a sum coefficient vector q_kWherein | | | Zu_k| | represents a calculation vector Zu_kThe upper label T represents the transpose of a matrix or vector;

③ according to formula u_new＝X_cq_k/q_k ²Calculating the vector u_new；

Fourthly, judging whether the condition is satisfied | | | u_k-u_new||＜10^-6(ii) a If not, put u_k＝u_newThen returning to the step II; if yes, executing a fifth step;

fifthly, according to the formula p_k＝Z^Ts_k/(s_k ^Ts_k) Calculating to obtain the k-th projection vector p_k∈R^(m-1)×1And preserving the projection vector p_kCoefficient vector w_kAnd a sum coefficient vector q_k；

Sixth, judge matrix Y_k＝s_kp_k ^TWhether the largest element in (a) is greater than 0.01; if so, according to the formula Z-S_kp_k ^TUpdating the matrix Z_iPerforming step (c); if not, obtaining a projection matrix P ═ P₁，p₂，…，p_k]And the coefficient matrix W ═ W₁，w₂，…，w_k]And the vector Q ═ Q₁，q₂，…，q_k]And executing the step (b);

seventhly, judging that k is less than m-m_c(ii) a If yes, after k is set to k +1, returning to the step II; if not, the final projection matrix P is obtained as [ P ]₁，p₂，…，p_k]And the coefficient matrix W ═ W₁，w₂，…，w_k]And the vector Q ═ Q₁，q₂，…，q_k]；

According to formula b_r＝W_r(P_r ^TW_r)^-1Q_r ^TCalculating a regression coefficient vector b under the condition of reserving r projection vectors_rWherein r is 1, 2, …,k，P_r、W_rand Q_rThe matrices P, W and the matrices formed by the first 1 to r column vectors in Q, respectively;

ninthly according to the formula

Computing output X_cPredicted value of (2)

Then, model prediction errors corresponding to different numbers of projection vectors are calculated and reserved

Wherein diag 2]Representing the operation of independently forming elements of a diagonal line of the matrix into a vector, and sum { } represents the summation of each element in the vector;

in the r in accordance with MSE₁，MSE₂，…，MSE_kFinding out the position of a convergence point of which the prediction error does not change remarkably any more according to the change condition of the numerical value, and taking a specific numerical value corresponding to a subscript number of the convergence point as the number K of projection variables needing to be reserved by the partial least square model, wherein K is less than or equal to K;

determining final input Y and output X according to K_cThe PLS model in between, namely:

X_c＝YW_K(P_K ^TW_K)^-1Q_K ^T+E_c＝YΘ_c+E_c (1)

in the above formula, the regression matrix Θ_c＝W_K(P_K ^TW_K)^-1Q_K ^T，

Is the regression model error.

3. The fault monitoring method based on the multi-production-unit variable cross-correlation decoupling strategy as claimed in claim 1, wherein the detailed implementation process of establishing the PCA fault monitoring model in the step (7) specifically comprises:

calculating

Covariance matrix of

Solving all the characteristic values gamma of S₁≥γ₂≥…≥γ_mCorresponding feature vector beta₁，β₂…，β_m；

Setting the number d of the reserved main components as the minimum value meeting the following conditions, and forming a diagonal matrix Lambda epsilon R by the corresponding d maximum eigenvalues^d×dAnd forming a projection transformation matrix B ═ beta by the corresponding d eigenvectors₁，β₂…，β_d]

Fourthly, D is calculated according to the formula shown in the specification_limAnd SPE_lim：

In the above two formulae, the confidence level α is 99%, F_α(d, n-d) represents a F distribution with degrees of freedom d and n-d,

represents the weight g ═ a/2b, and the degree of freedom h ═ 2a²χ of/b²Distribution, a and b are respectively

The estimated mean and the estimated variance of the corresponding statistic SPE.

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